The present invention relates generally to estimating system dynamics, and more particularly to a method of estimating system dynamics by measuring subsystem transfer functions of a system under test.
The dynamic performance of a structural system composed of a plurality of subsystems, such as a space satellite including a space bus and space payload, can be significantly affected by vibration or shock. The vibration or shock can damage or alter sensitive subsystems of the structural system. The need to understand the effects of vibration and shock on a particular subsystem, as well as on the structural system as a whole, is paramount to obtaining optimal dynamic performance.
Conventional methods perform detailed finite element modeling of all subsystems and the system as a whole in order to determine the effects vibration and shock will have on the system. Initially, a finite element model is generated for each subsystem. The subsystems are subsequently tested using shaker or tap excitation and motion (accelerometer) sensing in a free (suspended) or fixed (bolted to a surface) boundary condition. As the tests are performed, each subsystem finite model is tweaked to better match the test data in a process known as model updating. However, the model updating process provides an estimate of only limited accuracy regarding the effects of vibration and shock on a particular subsystem because the subsystem model never fully converges with the test data.
The tweaked subsystem finite element models are combined into a system model to predict the end-to-end system dynamics. This system model also has only limited system accuracy because it is based upon the individual subsystem models that were never made to fully match the subsystem test data. Regions of the system model that include high interaction between the subsystem models yield even poorer predictions of system dynamics.
After the complete system is built, but before the system is put to use (or launched as in the case of a satellite), a final dynamics test is conducted to verify model fidelity and to check end-to-end performance. Often, the test data is used to further refine the models of the individual parts. However, in the case of large or complex systems, the final dynamics and performance verification test are not feasible due to, for example, schedule or facility constraints.
In view of the above, the present invention provides a method of predicting system performance by performing subsystem dynamics testing to measure subsystem transfer functions, determining a system performance function based upon the subsystem transfer functions and determining a performance quantity at a specific point of interest from the system performance function. Transfer functions for each subsystem are measured at all degrees of freedom of interest while test forces are applied to each subsystem also at all degrees of freedom of interest. The degrees of freedom of interest include locations and directions where disturbance forces are injected (inputs), where motion affects system performance (outputs) and where the subsystem attaches to other subsystems (interfaces). A system performance function for the structural system as a whole is subsequently determined, and an end-to-end system performance transfer function can be determined based on the measured transfer functions of the subsystems. A system performance quantity can then be accurately estimated from each contributing disturbance.
Through the above method, the present invention provides a method of obtaining an accurate estimate of system performance without having to perform a final dynamics test of the actual system when shock or vibration is applied to individual subsystems within the system.